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تسجيل

Multiplicity

المؤلف:  Krantz, S. G

المصدر:  "Zero of Order n." §5.1.3 in Handbook of Complex Variables. Boston, MA: Birkhäuser

الجزء والصفحة:  p. 70

4-3-2019

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Multiplicity

The word multiplicity is a general term meaning "the number of values for which a given condition holds." For example, the term is used to refer to the value of the totient valence function or the number of times a given polynomial equation has a root at a given point.

Let  be a root of a function , and let  be the least positive integer  such that . Then the power seriesof  about  begins with the th term,

and  is said to have a root of multiplicity (or "order") . If , the root is called a simple root (Krantz 1999, p. 70).

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REFERENCES:

Krantz, S. G. "Zero of Order n." §5.1.3 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 70, 1999.